Expectation–maximisation approach to blind source separation of nonlinear convolutive mixture

Abstract

A novel learning algorithm for blind source separation of post-nonlinear convolutive mixtures is proposed. The proposed mixture model characterises both convolutive mixture and post-nonlinear distortions of the sources. A novel iterative technique based on a maximum likelihood approach is developed where the expectation-maximisation (EM) algorithm is generalised to estimate the parameters in the proposed model. In the E-step of the proposed framework, sufficient statistics of the posterior distribution of the source signals are estimated while the model parameters are optimised through these statistics in the M-step. The post-nonlinear distortions, however, render these statistics difficult to express in a closed form, and hence, this causes intractability in the M-step. A computationally efficient algorithm is further proposed to facilitate the E-step tractable and the self-updated multilayer perceptron is developed in the M-step to estimate the nonlinearity. The theoretical foundation of the proposed solution has been rigorously developed and discussed in detail. Both simulations and real-time speech signals have been used to verify the success and efficacy of the proposed algorithm. Remarkable improvement has been obtained when compared with the existing algorithm.